Recognition of finite groups by the prime graph
- 83 Downloads
We obtain the first example of an infinite series of finite simple groups that are uniquely determined by their prime graph in the class of all finite groups. We also show that there exist almost simple groups for which the number of finite groups with the same prime graph is equal to 2.
Keywordsprime graph finite group modular representations recognition
Unable to display preview. Download preview PDF.
- 2.A. Khosravi and B. Khosravi, “Quasirecognition of the simple group 2G2(q) by the prime graph,” to appear in Sib. Mat. Zh. Google Scholar
- 4.A. S. Kondratiev, “On prime graph components for finite simple groups,” Mat. Sb., 180, No. 6, 787–797 (1989).Google Scholar
- 11.The GAP Group, GAP — Groups, Algorithms, and Programming, Vers. 4.4.7 (2006); http: //www.gap-system.org.Google Scholar
- 13.B. Chang and R. Ree, “The character of G 2(q),” in Symp. Math., Vol. 13, Academic Press, London (1974), pp. 395–413.Google Scholar
- 17.B. Huppert and N. Blackburn, Finite Groups, Vol. 3, Springer, Berlin (1982).Google Scholar